In this screencast I am going to describe the steps used to obtain the work from a
steam turbine, and what the outlet conditions will be. This is for an irreversible turbine,
and so what I have drawn here is on a temperature/entropy diagram. The phase envelope separating 2 phase
region liquid and vapor from pure liquid or pure vapor. So our starting condition is
right here. This is the inlet condition to the turbine. It is in the superheated region.
So I have drawn a constant pressure line for the inlet conditions, and I have
drawn a constant pressure line for the outlet conditions. As we move through the turbine
the temperature decreases, because we are removing energy in the form of work from the
steam, and the entropy increases. This is an irreversible process. So this is the outlet
condition, at this point here. So in order to calculate the work what we are going to first
do is do the calculation for a reversible process. The first step in order to do that
is to determine the inlet conditions. So we need the inlet enthalpy and the inlet entropy,
and we are going to get those from the steam tables, and we get those because we know the
pressure and the temperature of the starting system, and as I mentioned the steam tables
will be for the superheated steam tables for our initial condition. So our second step
is to do the calculation for the reversible. So what we want to calculate is the outlet
condition. I am going to call this outlet prime. This is reversible case. This dash
line is the irreversible, and remember the irreversible corresponds to the actual process
that we are interested in. What I want to calculate is the outlet. So lets call that S prime at
the outlet, and that's going to be the same as S in because it is reversible, and it is
adiabatic. So our next step then, since we know the outlet pressure. That would be given
in our problem statement. We now know the outlet entropy. We have two properties of
steam or water, and I need two properties then that uniquely determine all the other
properties, and so we can determine, again from the stream tables, H prime out, the enthalpy
out if we ran the reversible process, so we get that from the steam tables. We are able
to get that because we know the pressure leaving, and we know S prime out. Our next
step is to calculate the work for the reversible process. So the reversible work is going to
be enthalpy out prime because it is reversible minus enthalpy in, and this number is going
to be less than zero, because we are getting work out of the system. So the work is going
to be negative for the system. So now we have the reversible work, and we need to determine
work for the actual system for the irreversible process. So the work for the actual system.
Let's call it irreversible, is going to be some efficiency times the reversible work, and
this needs to be given. This is a property of the system, it's some value less than one, because
it is irreversible. So once we are given that we can calculate the irreversible work.
One of our objectives is to calculate the irreversible work for this process. Now we can calculate
the outlet condition, and we do that from the first law, because the irreversible work is
going to be H out minus H in. So this H out of course corresponds to this point here.
We know the irreversible work, we know H in, so we can calculate H out just from this first
law. So now we have H out, and pressure out. Which means we can go to the steam tables.
Again we have 2 properties that uniquely determine the system properties. So we now
can determine other properties of the system; entropy out, T out, et cetera. So that basically
completes the procedure. The idea is that we first do the calculation for reversible
process, and then we take advantage of information about how irreversible, by knowing what the
efficiency is to calculate the conditions for the irreversible process.